Answer to Essential Question 23.1: To explain the formation of your own shadow on a sunny day, we can treat the Sun as a point source located 150 million km away. On the other hand, the shadow that the Earth casts on the Moon during a lunar eclipse has a very dark region (the umbra) and a semi-dark region (the penumbra). This more complex shadow pattern can be partly explained by treating the Sun as a distributed source.

23-2 The Law of ; Plane A of light that reflects from a surface obeys a very simple rule, known as the law of reflection. See, also, the illustrations in Figure 23.7. Figure 23.7: In each case, the ray obeys the Law of Reflection, in that the angle of The Law of Reflection: for a ray of light reflecting from incidence, measured from the normal, is equal a surface, the angle of incidence is equal to the angle of to the angle of reflection. In the specific reflection. These angles are generally measured from the examples shown, both the incident ray and the normal (perpendicular) to the surface. reflected ray are at an angle, measured from the normal, of (a) 60°, (b) 45°, and (c) 30°.

A surface acts as a when the law of reflection is followed on a large scale, as shown in Figure 23.8: (a) Specular Figure 23.8 (a). In that case, the whole beam of light, reflection from a flat mirror, with many parallel rays, reflects as expected according in which all rays reflect at the to the law. This is known as : same angle. (b) Many flat mirror-like reflection that preserves the wave-front surfaces exhibit diffuse structure. In Figure 23.8 (b), however, the surface does reflection, in which rays not seem to obey the law of reflection. If we look at the reflect at different angles. (c) magnified view, in (c), however, we see that the surface A magnified view of the is irregular. The law of reflection is obeyed for each ray situation in (b). Even though individually, but the irregularities in the surface cause the surface may appear flat to the rays to move off in many different directions after us, the surface is actually being reflected. This is known as diffuse reflection: quite irregular as far as light reflection in which the wave fronts are not preserved. is concerned. Diffuse reflection explains why some surfaces that appear to be flat, such as a table or a road, do not act as mirrors. As far as light is concerned, these surfaces are far from flat.

The surface in Figure 23.8(a) is known as a plane mirror. Common examples are the mirrors in every bathroom. When we look at ourselves in such a mirror, where do we see our image? How large is the image? To answer such questions, we can use a ray diagram to determine where an image is formed and what its characteristics are.

EXPLORATION 23.2 – Using a ray diagram to find the location of an image

Step 1 – An arrow is placed in front of a vertical plane mirror, as shown in Figure 23.9. Sketch two rays of light, which travel in different directions, that leave the tip of the arrow and reflect off the mirror. Show the direction of these rays after they reflect from Figure 23.9: An arrow located some the mirror. distance in front of a plane mirror.

Chapter 23 – Reflection and Mirrors Page 23 - 4 Figure 23.10 shows a number of rays leaving the arrow and reflecting from the mirror, obeying the law of reflection. One of these, the horizontal ray, in red, that strikes the mirror at a 0° angle of incidence (measured from the normal to the mirror) is special, in that it reflects back along the path the ray came in on, and is thus easy to draw. However, you do not need to use this particular ray in the ray Figure 23.10: A selection of reflected diagram – any two rays of light that reflect from the mirror can be rays. In each case, the reflected rays are used. drawn in the direction that is consistent with the law of reflection. Step 2 – The point where the reflected rays meet is where the tip of the image is located. Sketch the image of the arrow. The reflected rays diverge as they travel away from the mirror to the left, but if we extend the reflected rays back through the mirror to the right, we find a point where they intersect. This is where the image of the tip of the arrow is located. Note that all the reflected rays, when they are extended back, pass through this point, which is why we can use any two reflected rays to create the ray diagram. Because the base of the arrow, which we call the object, is located on the principal axis (the horizontal line bisecting the mirror), we know that the base of the image will Figure 23.11: For a plane mirror, the also be located there, so we draw an image of the arrow reflected rays must be extended back between the point where the image of the tip is and the through the mirror to find the location principal axis. where they meet. Because the rays left the tip of the arrow, the point where the reflected rays meet is the location of the tip Step 3 – Prove that the image is located of the image of the arrow. as shown in Figure 23.11 by drawing two more ray diagrams, one showing Figure 23.12: No matter the location of the image of the which point on the object midpoint of the arrow, and one showing the rays start from, the the location of the image of the base reflected rays can be (bottom) of the arrow. Figure 23.12 extended back to meet to combines the ray diagram for the tip with the right of the mirror. those of the arrow’s base and midpoint, showing that the image really is at the location shown in Figure 23.11. Figure 23.13: Our Step 4 – Compare the reflected rays in brains trace the reflected Figure 23.12 to the rays in Figure 23.6. rays back along straight Our brains cannot tell the difference lines until they meet, and between the two situations, which is why we see an image at that we see an image of the arrow formed at location. the location shown in Figure 23.13.

Key idea for ray diagrams: The location of the image of any point on an object, when the image is created by a mirror, can be found by drawing rays of light that leave that point on the object and reflect from the mirror. The direction of the reflected rays must be consistent with the law of reflection. The point where the reflected rays meet is where the image of that point is. Related End-of-Chapter Exercises: 1, 2, 5, 14.

Essential Question 23.2: First, make a prediction. When the arrow in Exploration 23.2 is moved closer to the mirror, will its image be larger, smaller, or the same size as the image we found in Step 2 above? Sketch a new ray diagram to check your prediction.

Chapter 23 – Reflection and Mirrors Page 23 - 5